Gases

Essential Questions

• • • • What are the properties of gases?

What does kinetic molecular theory mean to me?

How are temperature, pressure, and volume related?

How do gases affect our lives every day?

Properties of Gases

• • • • • Have mass Can be compressed – Compression: a measure of how much a volume of matter decreases under pressure. – Why can gases be compressed??

Expand to fill their containers Diffuse Exert pressure

Kinetic Molecular Theory

• • • Kinetic = motion Molecular = molecules Kinetic Molecular Theory explains the motion of ideal gas particles

Kinetic Molecular Theory

• • Explains why gases act the way they do Only works on an Ideal Gas More to come on that…

Kinetic Molecular Theory

• Assumption #1: • Gases are composed of a large number of tiny particles that are so far apart that individually, their volume is considered to be zero.

• Volume is always the volume of the container

Kinetic Molecular Theory

• Assumption #2: • Collisions between the particles and the walls of the container cause pressure.

• Small container = more collisions = more pressure

Kinetic Molecular Theory

• Assumption #3 • Gas particles move in straight lines and have perfectly elastic collisions • Particles are not attracted or repelled by each other • Particles don’t lose any energy when they hit each other or the walls of the container.

Kinetic Molecular Theory

• Assumption #4: • • The average kinetic energy of a number of gas particles is directly related to the temperature If Temperature  then Energy  • More Later

Ideal Gas??

• We use Kinetic Molecular Theory to describe the behavior of ideal gases only

Ideal Gas?

• In real life: • Particles do not have perfectly elastic collisions • Particles can have some attraction/repulsion, • Because they are moving so fast, we can pretend there is no attraction/repulsion • Using real gases, there are too many variables to account for. Using ideal gases we can explain behavior to a close approximation.

What About Mass?

• • • Gases have mass Very low density, so we don’t notice it You can feel the mass of a gas when there are a LOT of gas particles in a small amount of space (ever pick up a helium tank or wonder why they are always on hand-trucks?)

Pressure

• • • Pressure = force per unit area Things that affect pressure – Amount of gas – Volume – Temperature The Gas Laws will explain these relationships

Pressure Units

• • • • Sometimes, you need to convert between them 1 atmosphere = 760 mm Hg 1 mm Hg = 1 torr 1 atm = 101,325 Pascals (Pa) = 101.325 kPa

Pressure Calculations

• • • What is 724 mm Hg in torr?

– 724 torr In atm?

– 0.953 atm In kPa?

– 96.5 KPa

Unit Summary of Units of Pressure Abbreviation Unit Equivalent to 1 atm

atm 1 atm Atmosphere Millimeters of Hg Torr mm Hg torr 760 mm Hg 760 torr Pascal Kilopascal Pa kPa 101,325 Pa 101.325 kPa

Vacuum 1 atm Pressure

Barometer

• Measures air pressure

760 mm Hg

• The pressure of the atmosphere at sea level will hold a column of mercury 760 mm Hg.

• 1 atm = 760 mm Hg

Gas

h

Manometer

• • • Column of mercury to measure pressure of a gas One end has gas, the other is open h is how much lower the pressure of the gas is than atmosphere

Gas h

Manometer

• h is how much higher the gas pressure is than the atmosphere.

Reading a Manometer

Gas Laws

• Occasionally, gas Laws describe the behavior of gases at Standard Temperature and Pressure (STP) • 0° C • 273K • 1 atmosphere • 1 atm = 760 torr = 760 mmHg

BE CAREFUL!!!!

Temperature must

ALWAYS be in KELVIN!

Boyle’s Law

• • • • Boyle’s Law – Pressure and Volume P 1 V 1 = P 2 V 2 One increases, the other decreases Temperature must be constant

Try these…

• • A sample of gas starts out at a pressure 1.5 atm and a volume of 1.0 liter. If the pressure is increased to 2.0 atm, what is the volume of the gas?

• 0.75 atm A gas occupies 16 liters and has a pressure of 875 torr. If the volume is decreased to 5.0 liters, what is the new pressure of the gas?

• 2800 torr

Charles’ Law

• • • Charles’ Law – Temperature and Volume V 1 = V 2 T 1 T 2 One increases, the other increases Temperature must be in Kelvin, Pressure must remain constant

Try these…

• • A 2.00 liter sample of gas at 298 K is heated to 320 K. Pressure is constant at 1.00 atm. What is the new volume of the gas?

• 2.15L

Nicholas blows a soap bubble containing air at 42°C and has a volume of 23cm 3 at 1 atm. The bubble encounters a pocket of cold air at 18°C. What is the new volume of the soap bubble?

• 21cm 3

Gay-Lussac’s Law

• • • Gay-Lussac’s Law – Pressure and Temperature P 1 = P 2 T 1 T 2 One increases, the other increases Volume must remain constant

Try these…

• • If a 3.00L container contains a gas at 1.00 atm of pressure at 298 K, and the temperature is increased to 460 K, what is the pressure the gas exerts on the container?

• 1.54 atm If a 2L container starts out having a pressure of 870. torr at a temperature of 350. K, what is the temperature if the pressure decreases to 600. torr?

• 241 K

COMBINE them all together…

• Combined Gas Law P 1 V 1 T 1 = P 2 T V 2 2 • Most useful, because it brings all the other gas laws we’ve talked about together

Try these…

• • If I have a gas at a pressure of 12.0 atm, a volume of 23.0 liters, and a temperature of 200. K, and I raise the pressure to 14.0 atm and increase the temperature to 300. K, what is the new volume of the gas?

• 29.6 L A gas takes up 17.0 liters, has a pressure of 2.30 atm, and a temperature of 299 K. If I raise the temperature to 300. K and lower the pressure to 1.50 atm, what is the new volume of the gas?

• 26.2 L

Let’s get moles involved… Avogadro’s Law

• • At a constant temperature and pressure, volume relates directly to the number of moles More gas = more volume V 1 n 1 = V 2 n 2

Let’s put more stuff together…

• Ideal Gas Law • R is the ideal gas constant • What is R?

• R = 0.08206 (L·atm)/(mol·K) • With different units: • R = 8.31 (L·kPa)/(mol·K) • If you know 3 pieces of information about your gas you can calculate the fourth

Try these…

• • • If I have a 6.7mol of a gas at 350 K and 12 atm of pressure, what is the volume of the gas?

• 16L How many moles of gas will occupy 14 liters at 298 K and 2.0 atm of pressure?

• 1.1 mol At what pressure will 6.02 moles of gas occupy 3.14 liters at 98.0°C?

• 58.4 atm

Dalton’s Law

• • • • The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container.

The total pressure is the sum of the partial pressures.

P Total = P 1 + P 2 + P 3 For each P = nRT/V + P 4 + P 5 ...

Dalton's Law

• • • P Total = n 1 RT + n 2 RT + n 3 RT +...

V V V In the same container R, T and V are the same.

P Total = (n 1 + n 2 + n 3 +...) RT V • P Total = (n Total ) RT V

Dalton’s Law of Partial Pressure

Dalton’s Law Examples

• Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen at 101.30 kPa of total pressure if the partial pressures of nitrogen, carbon dioxide, and other gases are 79.10 kPa, 0.040 kPa, and 0.94 kPa, respectively?

– 21.22kPa

The mole fraction

• • • Ratio of moles of the substance to the total moles.

Symbol is Greek letter chi c c 1 = n 1 n Total = P 1 P Total

Examples

• • The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole fraction of nitrogen?

– 0.787

What is the partial pressure of nitrogen if the container holding the air is compressed to 5.25 atm?

– 4.13 atm

Review

• • • • • • • • • Properties of gases Kinetic Molecular Theory Boyle’s Law Charles’s Law Gay-Lussac’s Law Combined Gas Law Ideal Gas Law Dalton’s Law of Partial Pressures Mole Fraction

Stoichiometry

• • • • Our old friend… When you calculate volume in a stoichiometry problem using 22.4 L/mol, we are getting the volume at STP We will do all our stoichiometry problems at STP You can use gas laws to find the volume of product at different temperatures/pressures

Examples

• • Sulfur trioxide is produced in enormous quantities each year for use in the synthesis of sulfuric acid S (s) + O 2(g)  SO 2(g) 2SO 2(g) + O 2(g)  2SO 3(g) What volume of O 2(g) at 350°C and a pressure of 5.25atm is needed to completely convert 5.00g or sulfur to sulfur trioxide?

Examples

• • • Consider the following reaction: 4NH 3 (g) + 5O 2 (g)  4NO(g) +6H 2 O(g) What volume of NO at STP will be produced from 23.7L of NH 3 ?

– 23.7L

What volume of O 2 measured at STP will be consumed when 10.0L NH 3 is reacted?

– 12.5L

Examples

• • • Mercury can be produced by the following reaction: 2HgO  2Hg +O 2 What volume of oxygen gas can be produced from 4.10 g of mercury (II) oxide at STP?

– 0.212L

At 400.ºC and 740 torr?

– 0.537L